Public vehicles remained off the roads while major markets and educational institutions were forced to shut down in Kathmandu and other major cities in the strike called by hardline CPN-Maoist (Chand), led by Netra Bikram Chand.
Hundreds of security personnel were deployed in Kathmandu and surrounding areas to prevent violence during the protest, the first national strike since a devastating quake hit the country in April.
"Seven vehicles have been torched and another 19 vandalised," police spokesman Kamal Singh Bam said, adding that no casualties had been reported so far.
The nation-wide strike was called to oppose the Constitution drafting process initiated by the four major political forces, the Nepali Congress, CPN-UML, UCPN-Maoist and Madhesi Peoples Rights Forum Democratic after inking a 16-point deal.
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Nepal's Maoists struck a deal with rival parties on the new Constitution last month after years of bitter disagreement.
The demonstrators alleged that the Constitution does not address the problems of the ethnic, racial and gender discrimination.
The Maoist activists were also opposing an agreement between India and China to boost border trade at Qiangla/Lipu-Lekh Pass, close to an area which Nepal claims to be part of its territory.
Lipu-Lekh Pass, the last point of Nepal's border with China and India and known as an ancient route for traders and pilgrims transiting between Nepal and Tibet, is a far western point, near Kalapani, which is a disputed border area between Nepal and India.
The bandh enforcers today also vandalised a passenger bus in Maharajgunj and a milk-van in Gongobu, police said.
The strike also crippled life in Lalitpur, Bhaktapur, Banepa, Palpa and Hetauda.